Eating Healthy: Understanding Added Sugar through Proportional Reasoning

Research suggests that integrated STEM activities can best support students in developing their mathematical and scientific understanding. On one hand, while science provides mathematics with real-life authentic problems to investigate, mathematics provides science powerful tools to explore those problems. In line with this call, in this study, we designed an integrated lesson at the cross-section of proportional reasoning and added sugar present in food products to explore how added sugar provides students with a meaningful context to engage in proportional reasoning and how proportional reasoning helps students identify the quantity of added sugar present in different food products and provides students with a platform to initiate a conversation around quality of food products. Developed on the theoretical framework of Realistic Mathematics Education (RME), this lesson was remotely implemented on three middle school students. The result section highlights the design principle of the lesson that provided students with an opportunity to construct an understanding of both the disciplines through a mutual interaction.

Beyond the basics: a detailed conceptual framework of integrated STEM

Given the large variation in conceptualizations and enactment of K− 12 integrated STEM, this paper puts forth a detailed conceptual framework for K− 12 integrated STEM education that can be used by researchers, educators, and curriculum developers as a common vision. Our framework builds upon the extant integrated STEM literature to describe seven central characteristics of integrated STEM: (a) centrality of engineering design, (b) driven by authentic problems, (c) context integration, (d) content integration, (e) STEM practices, (f) twenty-first century skills, and (g) informing students about STEM careers. Our integrated STEM framework is intended to provide more specific guidance to educators and support integrated STEM research, which has been impeded by the lack of a deep conceptualization of the characteristics of integrated STEM. The lack of a detailed integrated STEM framework thus far has prevented the field from systematically collecting data in classrooms to understand the nature and quality of integrated STEM instruction; this delays research related to the impact on student outcomes, including academic achievement and affect. With the framework presented here, we lay the groundwork for researchers to explore the impact of specific aspects of integrated STEM or the overall quality of integrated STEM instruction on student outcomes.

Cultural Challenge: Teaching Mathematics to Non-mathematicians

A “mathematics for non-mathematicians” course, commonly known as a “service” course is an undergraduate mathematics course developed for students who are not (going to become) mathematics majors. Besides calculus, such courses may include linear algebra, mathematical reasoning, differential equations, mathematical programming and modeling, discrete mathematics, mathematics for teachers, and so on. In this article we argue that a good, productive curricular design and teaching of service courses happen through a meaningful collaboration between a mathematics instructor and the department whose students are taking the course. This collaboration ensures that “non-mathematicians” see the relevance of learning mathematics for their discipline (say, by discussing authentic problems and examples), but also appreciate the relevance and benefits which mathematics brings to their overall education and skills set.

Moving From Fragmented to Seamless Sense-Making in Blended Learning

Context: Sense-making, understood as meaning making or giving meaning to experience, is an integral part of everyday life, work and learning, and is a process critical in enabling people to recognise how and when to respond to situations appropriately so that they can resolve problems effectively (Weick et al., 2005). Earlier studies on sense-making in educational or organizational settings (e.g. Harverly et al., 2020; Weick et al., 2005) tended to focus on the sense-making process per se in particular setting such as classrooms or organizations, few of them have paid much attention to the sense-making process in blended learning (BL). BL in vocational training mainly aims to enable adult learners to apply what was learnt in classrooms to solve authentic problems in workplaces or simulated settings. High quality of sense-making is crucial to help the learners achieve the aim. This timely study is to offer a comparative look at how different dynamics of BL interplay together to mediate the quality of sense-making in achieving learning outcomes. The dynamics include industry and training connections, policy and institutional contexts, the inhabited pedagogical practices and curriculum design. Methods: This study adopted phenomenological (Moran, 2000) and semi-ethnographic approaches (Hammersley, 2010), including semi-structured interviews, observations, analysis of relevant documents (e.g. curriculum and learning materials) to capture the rich data in case studies to understand learners’ sense-making experience in BL. Researchers focused on seeking to understand how different environments, tools and artefacts mediate the quality of sense-making as the learners progressed through their learning journey. To triangulate the data, adult educators, curriculum designers and where possible, workplace supervisors, were also interviewed and observed for their perceptions and behaviours in learners’ sense-making in BL. Findings: The findings from two different BL courses (ICT and HR) surface that the degree to which learners’ sense-making is fragmented (low quality) or seamless (high quality) is mediated by the interplay of different contextual factors in BL in multiple ways, such as, the connections (or not) with industry, the use (or not) of authentic problems and tasks. Conclusion: The interplay between different dynamics in BL is of great importance to mediate the curriculum design and pedagogical approaches used in BL for high quality of sense-making of adult learners in vocational training.

Co-designing cross-setting activities in a large-scale STEM partnership program – Teachers’ and students’ experiences

STEM partnerships are popular initiatives but can be challenging to implement in practice. Accordingly, within the context of a nationwide, cross-setting STEM partnership program in Norway – Lektor2 – a co-design tool was introduced to support teachers to collaborate with STEM professionals in developing curriculum units involving authentic STEM problems and practices. Thus, the purpose of this study was to describe the teachers’ and students’ experiences from the curriculum units based on the co-design tool and how the tool might help facilitate partnerships in STEM education. Teacher and student data were collected in 2015-2018 (N= 2479), and responses to open-ended questions were coded using a grounded theory approach. Findings indicate that the co-design tool, particularly “the commission” – where students are commissioned by STEM professionals to design solutions to authentic problems – enhanced teachers’ collaboration with STEM professionals, led to changes in pedagogical approaches, and enabled the teachers to differentiate in their teaching. Student experiences from participating in the co-designed curriculum units are characterised as more expansive views of STEM, STEM learning, and increased STEM engagement. We discuss how the co-design tool enabled teachers to overcome partnership challenges and what aspects of the commission appeared to be important for the students’ experiences. This study provides a specific example of a co-design tool that can enhance pedagogical designs developed through STEM partnerships.

Engineering Students’ Perceptions of Mathematical Modeling in a Learning Module Centered on a Hydrologic Design Case Study

Engineering students need to spend time engaging in mathematical modeling tasks to reinforce their learning of mathematics through its application to authentic problems and real world design situations. Technological tools and resources can support this kind of learning engagement. We produced an online module that develops students’ mathematical modeling skills while developing knowledge of the fundamentals of rainfall-runoff processes and engineering design. This study examined how 251 students at two United States universities perceived mathematical modeling as implemented through the online module over a 5-year period. We found, subject to the limitation that these are perceptions from not all students, that: (a) the module allowed students to be a part of the modeling process; (b) using technology, such as modeling software and online databases, in the module helped students to understand what they were doing in mathematical modeling; (c) using the technology in the module helped students to develop their skill set; and (d) difficulties with the technology and/or the modeling decisions they had to make in the module activities were in some cases barriers that interfered with students’ ability to learn. We advocate for instructors to create modules that: (a) are situated within a real-world context, requiring students to model mathematically to solve an authentic problem; (b) take advantage of digital tools used by engineers to support students’ development of the mathematical and engineering skills needed in the workforce; and (c) use student feedback to guide module revisions.

Pre-service teacher’s mathematical knowledge for teaching in problem-based learning

Mathematical Knowledge for Teaching (MKT), comprising Mathematics Content Knowledge (MCK) and Mathematics Pedagogy Content Knowledge (MPCK), is essential for pre-service teachers. However, numerous studies have shown that pre-service teachers are weak in content and difficult to plan to teach. Therefore, a shifting effort dealing with the learning activities within the teacher training program from a teacher-centered to student-centered approach should be made. One learning model succeeding in the student-centered approach is Problem-Based Learning (PBL). Studies on PBL as an effort to improve the MCK and MPCK of pre-service teachers have never been done before. There were two models of PBL applied in this experimental study: PBL with authentic problems (PBL1) and PBL with authentic problems and teaching practices (PBL2). The aspects of MCK studied are knowing, applying, and reasoning. While the aspects of MPCK are creating representation for the explanation, understanding mathematical structures, and anticipating students' thinking. The results of the study showed that there were significant differences between MCK and MPCK achievements in PBL1, PBL2, and conventional learning classes conventional. PBL1 and PBL2 classes were considered superiors since the pre-service teachers predominantly control the learning activities and were active in finding solutions. Hence, there were differences in the effect of the learning models on the aspects of MCK and MPCK.

A study on the bridge of music intelligence to Chinese comprehension

This study aims to use the theory of multiple intelligences to explore the strategies of music intelligence bridging Chinese comprehension and their impacts on students’ learning. An action research was conducted since the purposes of this study are both to test multiple intelligences theory and to improve Chinese teaching. Several models and approaches have been developed to apply multiple intelligences theory into practice in K-8 classrooms. Baum et al (2005) identified five pathways to apply multiple intelligences theory in the elementary classroom; they are Explorations, Building on Strengths, Understanding, Authentic Problems, and Talent Development. While Viens and Kallenbach (2004) labeled the first fourth as MI Reflections, Bridging Students' Areas of Strengths to Areas of Challenge, Entry/Exit Points, and Projects. The approach of Bridging Students' Areas of Strengths to Areas of Challenge is to create a "bridge" from students' MI strengths to appropriate learning strategies, emphasizing using students' particular strengths to assist in areas of particular difficulty (Viens & Kallenbach, 2004). The models of Vocabulary-in-Song bridging Chinese reading comprehension was built and discussed. Teaching skills which must be coupled with the bridging model were discussed. The hope and limitation of Vocabulary-in-Song bridging Chinese reading comprehension were showed.

Smash-Up

Among the current trends, globally in education, is a focus on personalized learning as a way to meet student needs, increase engagement, and improve achievement. Design thinking is a process, as well as a way of being, which, as a promising practice, provides a means for personalizing learning through work that is meaningful and relevant to students. The mindsets and processes of design thinking were used to invite gifted students into problem finding and problem solving, which began with where the students were at and further developed their knowledge and skills in action-oriented solutions. Using design thinking, students engaged in the world to solve authentic problems through a lens of empathy and human centeredness, strengthening their ties to community. Design thinking provided rich learning opportunities that were effective for gifted learners, engaging their curiosity, sense of social justice, imagination, and critical thinking.